Inelastic collision processes driven by anistropic interactions are investigated below 1 K. Three distinct experiments are presented. First, for the atomic species antimony (Sb), rapid relaxation is observed in collisions with \(^4He\). We identify the relatively large spin-orbit coupling as the primary mechanism which distorts the electrostatic potential to introduce significant anisotropy to the ground \(^4S_{3/2}\) state. The collisions are too rapid for the experiment to fix a specific value, but an upper bound is determined, with the elastic-to-inelastic collision ratio \(\gamma \leq 9.1 x 10^2\). In the second experiment, inelastic \(\mathcal{m}_J\)-changing and \(J\)-changing transition rates of aluminum (Al) are measured for collisions with \(^3He\). The experiment employs a clean method using a single pump/probe laser to measure the steady-state magnetic sublevel population resulting from the competition of optical pumping and inelastic collisions. The collision ratio \(\gamma\) is measured for both \(\mathcal{m}_J\)- and \(J\)-changing processes as a function of magnetic field and found to be in agreement with the theoretically calculated dependence, giving support to the theory of suppressed Zeeman relaxation in spherical \(^2P_{1/2}\) states [1]. In the third experiment, very rapid atom-atom relaxation is observed for the trapped lanthanide rare-earth atoms erbium (Er) and thulium (Tm). Both are nominally nonspherical \((L \neq 0)\) atoms that were previously observed to have strongly suppressed electronic interaction anisotropy in collisions with helium \((\gamma > 10^4-10^5, [2,3])\). No suppression is observed in collisions between these atoms \((\gamma \lesssim 10)\), which likely implies that evaporative cooling them in a magnetic trap will be impossible. Taken together, these studies reveal more of the role of electrostatic anisotropy in cold atomic collisions.